In fact, the axion kinetic energy at the end of trapping is shown to be in general much larger than \(K_{\text{min}}\) .
Trapped misalignment then automatically seeds kinetic misalignment [1]} between
\(T\sim T_{\rm QCD}\)  and lower temperatures.
The axion rolls for a long time over the low-temperature potential barriers before final oscillations start at \(T\ll T_{\rm QCD}\) , extending further the delay of oscillations around the true minimum ensured by the trapped period.
In consequence, the trapped+kinetic misalignment mechanism enhances even more strongly the DM relic density.
